In data transmission systems, modems and multiplex equipment partition a serial data stream into two different sequences of bit groups: namely, symbols having M bits and frames having N bits. Typically, an integral number (M/N) of frames are grouped together to form a symbol.
A symbol clock signal synchronized with each symbol occurrence is also synchronized with each group of frames because of the integral relationship between symbols and frames. The symbol clock signal alone is necessary to recover each symbol in the modem and each frame in the multiplex equipment. Each similar transition of the symbol clock signal occurs at an identical position within each successive symbol. Hence, no ambiguity exists in using only the symbol clock signal to locate and define each frame because the symbol clock signal also coincides in phase once per symbol with an identical position of each successive integral number of frames comprising a symbol.
Known data transmission systems operate without ambiguity between the symbol clock and the frames only under the limited condition that each symbol includes an integral number of frames. A problem neither encompassed by the condition above nor addressed in the known prior systems occurs when a symbol includes a nonintegral number (M/N) of frames. In this situation, a so-called n-fold ambiguity arises with respect to the sequence of frames in the serial data stream because the beginning of a symbol and the beginning of a frame coincide only once every n symbols or n.multidot.M bits, where n equals N/GCD(N,M) and GCD(N,M) is the greatest common divisor of the two integers N and M. Consequently, the symbol clock signal traverses N complete cycles every M frames. That is, the symbol clock signal coincides in phase with identical positions in successive frames only once every n symbols, i.e., the n-fold ambiguity, as opposed to once every symbol in the prior systems.
Consequently, location and recovery of the frames and constituent data streams within consecutive frames is not possible in prior data transmission systems when a symbol includes a nonintegral number of frames because of the existing n-fold ambiguity between the symbol clock and the frame locations.